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   <h4 class="subsectionHead"><span class="titlemark">3.1   </span> <a 
 id="x21-670003.1"></a>2D Elements</h4>
<!--l. 1582--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.1   </span> <a 
 id="x21-680003.1.1"></a>Tr1ht element</h5>
<!--l. 1584--><p class="noindent" >Implements the linear triangular finite element for heat transfer problems. Each node has 1 degree of freedom. The
cross section thickness property is requested form cross section model. The node numbering is anti-clockwise. The
element features are summarized in Table&#x00A0;<a 
href="#x21-6800250">50<!--tex4ht:ref: Tr1htsummary --></a>.
<!--l. 1588--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x21-6800121"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure23.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;21: </span><span  
class="content">Tr1ht element - node and side numbering.</span></div><!--tex4ht:label?: x21-6800121 -->
                                                                                           
                                                                                           
<!--l. 1595--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1597--><p class="noindent" >
<div class="table">
<!--l. 1597--><p class="noindent" ><a 
 id="x21-6800250"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-52" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-52-1g"><col 
id="TBL-52-1"></colgroup><colgroup id="TBL-52-2g"><col 
id="TBL-52-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-52-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-52-1-2"  
class="td11"><!--l. 1597--><p class="noindent" ><span 
class="cmbx-10">Tr1ht</span>                                                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-2-2"  
class="td11"><!--l. 1597--><p class="noindent" >triangular finite element with linear approximation for heat
transfer problems                                                      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-52-3-2"  
class="td11"><!--l. 1597--><p class="noindent" >-                                                                            </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-52-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-4-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-4-2"  
class="td11"><!--l. 1599--><p class="noindent" >Single dof (T_f - temperature) is required in each node.    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-5-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-5-2"  
class="td11"><!--l. 1600--><p class="noindent" >Linear approximation of temperature.                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-6-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-6-2"  
class="td11"><!--l. 1601--><p class="noindent" >Integration using one point gauss integration formula.      </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-7-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-7-2"  
class="td11"><!--l. 1608--><p class="noindent" >Body loads are supported. Boundary loads are supported
and are computed using numerical integration. The side
numbering  is  following.  Each  i-th  element  side  begins
in  i-th  element  node  and  ends  on  next  element  node
(i+1-th  node  or  1-st  node,  in  the  case  of  side  number
3).  The  local  positive  edge  x-axis  coincides  with  side
direction, the positive local edge y-axis is rotated 90 degrees
anti-clockwise (see fig. (<a 
href="#x21-6800121">21<!--tex4ht:ref: Tr1htfig --></a>)).                                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-8-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-8-2"  
class="td11"><!--l. 1609--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-52-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-9-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-52-9-2"  
class="td11"><!--l. 1610--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-52-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-10-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-52-10-2"  
class="td11"><!--l. 1612--><p class="noindent" >                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-52-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-11-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-52-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-52-12-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;50: </span><span  
class="content">Tr1ht element summary</span></div><!--tex4ht:label?: x21-6800250 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.2   </span> <a 
 id="x21-690003.1.2"></a>Tr1mt element</h5>
<!--l. 1615--><p class="noindent" >Isoparametric triangular finite element with linear approximation of moisture. Other features are the same as for
Tr1ht in Section&#x00A0;<a 
href="#x21-680003.1.1">3.1.1<!--tex4ht:ref: Tr1ht --></a>.
<!--l. 1618--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.3   </span> <a 
 id="x21-700003.1.3"></a>Tr1hmt element</h5>
<!--l. 1619--><p class="noindent" >Isoparametric triangular finite element with linear approximations of temperature and moisture. Other features are
the same as for Tr1ht in Section&#x00A0;<a 
href="#x21-680003.1.1">3.1.1<!--tex4ht:ref: Tr1ht --></a>.
<!--l. 1624--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.4   </span> <a 
 id="x21-710003.1.4"></a>Quad1ht element</h5>
<!--l. 1626--><p class="noindent" >Represents isoparametric four-node quadrilateral finite element for heat transfer problems. Each node has 1 degree of
freedom. Problem should be defined in x,y plane. The cross section thickness property is requested form cross section
model. The nodes should be numbered anti-clockwise (positive rotation around z-axis). The element features are
summarized in Table&#x00A0;<a 
href="#x21-7100251">51<!--tex4ht:ref: Quad1htsummary --></a>.
<!--l. 1633--><p class="indent" >   <hr class="figure"><div class="figure" 
>
                                                                                           
                                                                                           
<a 
 id="x21-7100122"></a>
                                                                                           
                                                                                           
<!--l. 1--><p class="noindent" ><img 
src="elementlibmanual-figure24.png" alt="PIC"  
>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;22: </span><span  
class="content">Quad1ht element. Node numbering, Side numbering and definition of local edge c.s.(a).</span></div><!--tex4ht:label?: x21-7100122 -->
                                                                                           
                                                                                           
<!--l. 1642--><p class="indent" >   </div><hr class="endfigure">
<div class="center" 
>
<!--l. 1645--><p class="noindent" >
<div class="table">
<!--l. 1645--><p class="noindent" ><a 
 id="x21-7100251"></a><hr class="float"><div class="float" 
> <!--tex4ht:inline--><div class="tabular"> <table id="TBL-53" class="tabular" 
cellspacing="0" cellpadding="0" rules="groups" 
><colgroup id="TBL-53-1g"><col 
id="TBL-53-1"></colgroup><colgroup id="TBL-53-2g"><col 
id="TBL-53-2"></colgroup><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-53-1-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-1-1"  
class="td11"><span 
class="cmbx-10">Keyword         </span></td><td  style="white-space:wrap; text-align:left;" id="TBL-53-1-2"  
class="td11"><!--l. 1645--><p class="noindent" ><span 
class="cmbx-10">Quad1ht</span>                                                        </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-2-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-2-1"  
class="td11">Description          </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-2-2"  
class="td11"><!--l. 1645--><p class="noindent" >Isoparametric four-node quadrilateral linear interpolation
element for heat transfer problems                                </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-3-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-3-1"  
class="td11">Specific parameters</td><td  style="white-space:wrap; text-align:left;" id="TBL-53-3-2"  
class="td11"><!--l. 1645--><p class="noindent" >[<span 
class="cmtt-10">NIP</span>&#x00A0;#<span 
class="cmr-5">(in)</span>]                                                               </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-53-4-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-4-1"  
class="td11">Parameters           </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-4-2"  
class="td11"><!--l. 1646--><p class="noindent" ><span 
class="cmtt-10">NIP</span>: allows to change the default number of integration
point used.                                                              </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-5-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-5-1"  
class="td11">Unknowns            </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-5-2"  
class="td11"><!--l. 1647--><p class="noindent" >Single dof (T_f - temperature) is required in each node.    </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-6-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-6-1"  
class="td11">Approximation      </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-6-2"  
class="td11"><!--l. 1648--><p class="noindent" >Linear approximation of temperature.                           </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-7-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-7-1"  
class="td11">Integration           </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-7-2"  
class="td11"><!--l. 1651--><p class="noindent" >Integration  using  gauss  integration  formula  in  4  (the
default), 9, or 16 integration points. The default number
of  integration  point  used  can  be  overloaded  using  <span 
class="cmtt-10">NIP</span>
parameter.                                                               </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-8-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-8-1"  
class="td11">Loads                  </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-8-2"  
class="td11"><!--l. 1658--><p class="noindent" >Body loads are supported. Boundary loads are supported
and  computed  using  numerical  integration.  The  side
numbering  is  following.  Each  i-th  element  side  begins
in  i-th  element  node  and  ends  on  next  element  node
(i+1-th  node  or  1-st  node,  in  the  case  of  side  number
4).  The  local  positive  edge  x-axis  coincides  with  side
direction, the positive local edge y-axis is rotated 90 degrees
anti-clockwise (see fig. (<a 
href="#x21-7100122">22<!--tex4ht:ref: Quad1htfig --></a>)).                                       </td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-9-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-9-1"  
class="td11">Features              </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-9-2"  
class="td11"><!--l. 1659--><p class="noindent" >-                                                                            </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-53-10-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-10-1"  
class="td11">CS properties </td> <td  style="white-space:wrap; text-align:left;" id="TBL-53-10-2"  
class="td11"><!--l. 1660--><p class="noindent" >-</td>
</tr><tr  
 style="vertical-align:baseline;" id="TBL-53-11-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-11-1"  
class="td11">Status                 </td><td  style="white-space:wrap; text-align:left;" id="TBL-53-11-2"  
class="td11"><!--l. 1662--><p class="noindent" >                                                 </td></tr><tr  
 style="vertical-align:baseline;" id="TBL-53-12-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-12-1"  
class="td11"> </td>
</tr><tr 
class="hline"><td><hr></td><td><hr></td></tr><tr  
 style="vertical-align:baseline;" id="TBL-53-13-"><td  style="white-space:nowrap; text-align:left;" id="TBL-53-13-1"  
class="td11">                </td></tr></table></div>
<br /> <div class="caption" 
><span class="id">Table&#x00A0;51: </span><span  
class="content">Quad1ht element summary</span></div><!--tex4ht:label?: x21-7100251 -->
</div><hr class="endfloat" />
</div>
</div>
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.5   </span> <a 
 id="x21-720003.1.5"></a>Quad1mt element</h5>
<!--l. 1665--><p class="noindent" >Isoparametric four-node quadrilateral finite element. Other features are the same as for Quad1ht in
Section&#x00A0;<a 
href="#x21-710003.1.4">3.1.4<!--tex4ht:ref: Quad1ht --></a>.
<!--l. 1668--><p class="noindent" >
   <h5 class="subsubsectionHead"><span class="titlemark">3.1.6   </span> <a 
 id="x21-730003.1.6"></a>Quad1hmt element</h5>
<!--l. 1669--><p class="noindent" >Represents isoparametric four-node quadrilateral finite element for heat and mass (one constituent) transfer
problems. Two dofs (T_f - temperature and C_1 - concentration) are required in each node. Linear
approximation of temperature and mass concentration. Other features are similar to Quad1 element, see section
<a 
href="#x21-710003.1.4">3.1.4<!--tex4ht:ref: Quad1ht --></a>.
                                                                                           
                                                                                           
                                                                                           
                                                                                           
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